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A277069 Decimal expansion of the real part of the root of the function x^y = y. 1
9, 9, 1, 1, 2, 0, 1, 4, 7, 9, 9, 1, 8, 7, 7, 4, 0, 4, 6, 9, 5, 2, 5, 2, 3, 9, 8, 9, 0, 4, 7, 7, 4, 4, 1, 8, 7, 2, 5, 9, 9, 7, 7, 6, 4, 1, 9, 5, 1, 3, 1, 5, 7, 5, 6, 7, 2, 3, 7, 3, 1, 2, 9, 2, 5, 9, 5, 2, 5, 4, 7, 5, 9, 9, 9, 8, 2, 5, 0, 9, 0, 9, 0, 5, 3, 1, 6, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

This value is negative.

It is not known if this number has a closed form.

This root occurs on the real component of the function x^y = y for x values which are all real.

LINKS

Table of n, a(n) for n=2..89.

FORMULA

Original fixed point function is of the form: x^y = y. When solved for y: y = -ProductLog(-log(x))/log(x).

EXAMPLE

-99.1120147991877404695252398904774418725997764195131575672373129...

MATHEMATICA

FindRoot[Re[-ProductLog[-Log[x]]/Log[x]], {x, -100, -99}, WorkingPrecision -> 261]

CROSSREFS

Cf. A277067.

Sequence in context: A229758 A076115 A014726 * A197503 A197401 A197350

Adjacent sequences:  A277066 A277067 A277068 * A277070 A277071 A277072

KEYWORD

nonn,cons

AUTHOR

David D. Acker, Sep 27 2016

STATUS

approved

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Last modified June 19 10:32 EDT 2019. Contains 324219 sequences. (Running on oeis4.)